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- 1. ANALYTICAL GEOMETRY SJ van Heerden 09/03/2014
- 2. HISTORY Introduced in the 1630s Aided the development of calculus RENE DESCARTES (1596-1650) and PIERRE DE FERMAT (1601-1665), French mathematicians, independently developed the foundations for analytical geometry
- 3. CARTESIAN PLANE
- 4. • x-axis (horizontal axis) where the x values are plotted along. • y-axis (vertical axis) where the y values are plotted along. • origin, symbolized by 0, marks the value of 0 of both axes • coordinates are given in the form (x,y) and is used to represent different points on the plane.
- 5. Slope of a Line
- 6. Slope of a Line
- 7. Slope of a Line
- 8. Slope of a Line
- 9. Slope of a Line
- 10. Inclination of a Line y y L L θ O M x θ O M x
- 11. Angle between Two Lines
- 12. Angle between Two Lines • If θ is angle, measured counter-clockwise, between two lines, then • where m2 is the slope of the terminal side and m1 is the slope of the initial side
- 13. SLOPE OF PARALLEL LINES
- 14. SLOPE OF PERPENDICULAR LINES
- 15. Sample Problems
- 16. EQUATION OF A CIRCLE
- 17. EQUATION OF CIRCLE (origin is not the center) A (h, k) B ( x, y)
- 18. Graph the following circle.
- 19. REFERENCES - Demirdag, M. (2013). Analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/mstfdemirdag/analytic-geometry-8693115. Accessed on: 4 March 2014 - Felipe, N, M. (2013). Analytic geometry basic concepts [PowerPoint Presentation]. Available at: http://www.slideshare.net/NancyFelipe1/analytic-geometry-basic-concepts.Accessed on: 4 March 2014 - Marasigan, D. (2013). Lecture #2 analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/denmarmarasigan/lecture-2-analytic-geometry.Accessed on: 4 March 2014 - Marasigan, D. (2013). Lecture #3 analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/denmarmarasigan/lecture-3-analytic-geometry.Accessed on: 4 March 2014 - Marasigan, D. (2013). Lecture #5 analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/denmarmarasigan/lecture-5-analytic-geometry. Accessed on: 4 March 2014

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